Statistics Solutions

[Steps Shown] Let 0 > a > b. Define a 1 = a, b 1 = b, and then define inductively a n+1 = for n ≥ 1. Prove that a n ≥ a n+1 ≥ b n+1 ≥ b n for all n ≥ 1 (Hint prove

Question: Let 0 > a > b. Define

a ₁ = a, b ₁ = b,

and then define inductively

a _n+1 =

for n ≥ 1.

Prove that
a _n ≥ a _n+1 ≥ b _n+1 ≥ b _n
for all n ≥ 1 ( Hint prove first that for any
Conclude that both a _n and b _n are convergent
Call

a ^* = and b ^* = .

Prove that a ^* = b ^*

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[Steps Shown] Let 0 > a > b. Define a 1 = a, b 1 = b, and then define inductively a n+1 = for n ≥ 1. Prove that a n ≥ a n+1 ≥ b n+1 ≥ b n for all n ≥ 1 (Hint prove

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